Christopher R. Iacovella

Hydrodynamics and microphase ordering in block copolymers: Are hydrodynamics required for ordered phases with periodicity in more than one dimension?

We use Brownian dynamics (BD), molecular dynamics, and dissipative particle dynamics to study the phase behavior of diblock copolymer melts and to determine if hydrodynamics is required in the formation of phases with greater than one-dimensional periodicity. We present a phase diagram for diblock copolymers predicted by BD and provide a relationship between the inverse dimensionless temperature epsilon/k(B)T and the Flory-Huggins chi parameter, allowing for a quantitative comparison between methods and to mean field predictions. Our results concerning phase behavior are in good qualitative agreement with the theoretical predictions of Matsen and Bates [M. W. Matsen and F. S. Bates, Macromolecules 29, 1091 (1996)]; however, fluctuation effects arising from finite polymer lengths substantially alter the phase boundaries. Our results pertaining to the hydrodynamics are in contrast to earlier work by Groot et al. [R. D. Groot, T. J. Madden, and D. J. Tildesley, J. Chem. Phys. 110, 9739 (1999); D. Frenkel and B. Smit, Understanding Molecular Simulation, 2nd ed. (Academic, New York, 2001)]. In particular, we obtain the hexagonal ordered cylinder phase with BD, a method that does not include hydrodynamics.

Self Assembly of Soft Matter Quasicrystals and Their Approximants

The surprising recent discoveries of quasicrystals and their approximants in soft-matter systems poses the intriguing possibility that these structures can be realized in a broad range of nanoscale and microscale assemblies. It has been theorized that soft-matter quasicrystals and approximants are largely entropically stabilized, but the thermodynamic mechanism underlying their formation remains elusive. Here, we use computer simulation and free-energy calculations to demonstrate a simple design heuristic for assembling quasicrystals and approximants in soft-matter systems. Our study builds on previous simulation studies of the self-assembly of dodecagonal quasicrystals and approximants in minimal systems of spherical particles with complex, highly specific interaction potentials. We demonstrate an alternative entropy-based approach for assembling dodecagonal quasicrystals and approximants based solely on particle functionalization and shape, thereby recasting the interaction-potential-based assembly strategy in terms of simpler-to-achieve bonded and excluded-volume interactions. Here, spherical building blocks are functionalized with mobile surface entities to encourage the formation of structures with low surface contact area, including non-close-packed and polytetrahedral structures. The building blocks also possess shape polydispersity, where a subset of the building blocks deviate from the ideal spherical shape, discouraging the formation of close-packed crystals. We show that three different model systems with both of these features—mobile surface entities and shape polydispersity—consistently assemble quasicrystals and/or approximants. We argue that this design strategy can be widely exploited to assemble quasicrystals and approximants on the nanoscale and microscale. In addition, our results further elucidate the formation of soft-matter quasicrystals in experiment.

Complex crystal structures formed by the self-assembly of ditethered nanospheres.

We report the results from a computational study of the self-assembly of amphiphilic ditethered nanospheres using molecular simulation. As a function of the interaction strength and directionality of the tether-tether interactions, we predict the formation of four highly ordered phases not previously reported for nanoparticle systems. We find a double diamond structure comprised of a zinc blende (binary diamond) arrangement of spherical micelles with a complementary diamond network of nanoparticles (ZnS/D), a phase of alternating spherical micelles in a NaCl structure with a complementary simple cubic network of nanoparticles to form an overall crystal structure identical to that of AlCu2Mn (NaCl/SC), an alternating tetragonal ordered cylinder phase with a tetragonal mesh of nanoparticles described by the [8,8,4] Archimedean tiling (TC/T), and an alternating diamond phase in which both diamond networks are formed by the tethers (AD) within a nanoparticle matrix. We compare these structures with those observed in linear and star triblock copolymer systems.

Characterizing Structure Through Shape Matching and Applications to Self-Assembly

Structural quantities such as order parameters and correlation functions are often employed to gain insight into the physical behavior and properties of condensed matter systems. Although standard quantities for characterizing structure exist, often they are insufficient for treating problems in the emerging field of nano- and microscale self-assembly, wherein the structures encountered may be complex and unusual. The computer science field of shape matching offers a robust solution to this problem by defining diverse methods for quantifying the similarity between arbitrarily complex shapes. Most order parameters and correlation functions used in condensed matter apply a specific measure of structural similarity within the context of a broader scheme. By substituting shape matching quantities for traditional quantities, we retain the essence of the broader scheme, but extend its applicability to more complex structures. Here we review some standard shapematching techniques and discuss how they might be used to create highly flexible structural metrics for diverse systems such as self-assembled matter. We provide three proof-of-concept example problems applying shape-matching methods to identifying local and global structures and tracking structural transitions in complex assembled systems. The shape-matching methods reviewed here are applicable to a wide range of condensed matter systems, both simulated and experimental, provided particle positions are known or can be accurately imaged.

Derivation of coarse-grained potentials via multistate iterative Boltzmann inversion.

In this work, an extension is proposed to the standard iterative Boltzmann inversion (IBI) method used to derive coarse-grained potentials. It is shown that the inclusion of target data from multiple states yields a less state-dependent potential, and is thus better suited to simulate systems over a range of thermodynamic states than the standard IBI method. The inclusion of target data from multiple states forces the algorithm to sample regions of potential phase space that match the radial distribution function at multiple state points, thus producing a derived potential that is more representative of the underlying interactions. It is shown that the algorithm is able to converge to the true potential for a system where the underlying potential is known. It is also shown that potentials derived via the proposed method better predict the behavior of n-alkane chains than those derived via the standard IBI method. Additionally, through the examination of alkane monolayers, it is shown that the relative weight given to each state in the fitting procedure can impact bulk system properties, allowing the potentials to be further tuned in order to match the properties of reference atomistic and/or experimental systems.

Local ordering of polymer-tethered nanospheres and nanorods and the stabilization of the double gyroid phase

We present results of Brownian dynamics simulations of tethered nanospheres and tethered nanorods. Immiscibility between tether and nanoparticle facilitates microphase separation into the bicontinuous, double gyroid structure (first reported by Iacovella et al. [Phys. Rev. E 75, 040801(R) (2007)] and Horsch et al. [J. Chem. Phys. 125, 184903 (2006)], respectively). We demonstrate the ability of these nanoparticles to adopt distinct, minimal energy local packings, in which nanospheres form icosahedral-like clusters and nanorods form splayed hexagonal bundles. These local structures reduce packing frustration within the nodes of the double gyroid. We argue that the ability to locally order into stable structures is key to the formation of the double gyroid phase in these systems.

Stability of the double gyroid phase to nanoparticle polydispersity in polymer-tethered nanosphere systems

Recent simulations predict that aggregating nanospheres functionalized with polymer “tethers” can self-assemble to form the double gyroid (DG) phase seen in block copolymer and surfactant systems. Within the struts of the gyroid, the nanoparticles pack in icosahedral motifs, stabilizing the gyroid phase in a small region of the phase diagram. Here, we study the impact of nanoparticle size polydispersity on the stability of the double gyroid phase. We show for low amounts of polydispersity the energy of the double gyroid phase is lowered. A large amount of polydispersity raises the energy of the system, disrupts the icosahedral packing, and eventually destabilizes the gyroid. Our results show that the DG forms readily up to 10% polydispersity. Considering polydispersity as high as 30%, our results suggest no terminal polydispersity for the DG, but that higher polydispersities may kinetically inhibit the formation of phase. The inclusion of a small population of either smaller or larger nanospheres encourages low-energy icosahedral clusters and increases the gyroid stability while facilitating its formation. We also introduce a new measure for determining the volume of a component in a microphase-separated system based on the Voronoi tessellation.

Structural Origins of Conductance Fluctuations in Gold-Thiolate Molecular Transport Junctions.

We report detailed atomistic simulations combined with high-fidelity conductance calculations to probe the structural origins of conductance fluctuations in thermally evolving Au-benzene-1,4-dithiolate-Au junctions. We compare the behavior of structurally ideal junctions (where the electrodes are modeled as flat surfaces) to structurally realistic, experimentally representative junctions resulting from break-junction simulations. The enhanced mobility of metal atoms in structurally realistic junctions results in significant changes to the magnitude and origin of the conductance fluctuations. Fluctuations are larger by a factor of 2-3 in realistic junctions compared to ideal junctions. Moreover, in junctions with highly deformed electrodes, the conductance fluctuations arise primarily from changes in the Au geometry, in contrast to results for junctions with nondeformed electrodes, where the conductance fluctuations are dominated by changes in the molecule geometry. These results provide important guidance to experimentalists developing strategies to control molecular conductance, and also to theoreticians invoking simplified structural models of junctions to predict their behavior.

Large-scale atomistic simulations of environmental effects on the formation and properties of molecular junctions.

Using an updated simulation tool, we examine molecular junctions composed of benzene-1,4-dithiolate bonded between gold nanotips, focusing on the importance of environmental factors and interelectrode distance on the formation and structure of bridged molecules. We investigate the complex relationship between monolayer density and tip separation, finding that the formation of multimolecule junctions is favored at low monolayer density, while single-molecule junctions are favored at high density. We demonstrate that tip geometry and monolayer interactions, two factors that are often neglected in simulation, affect the bonding geometry and tilt angle of bridged molecules. We further show that the structures of bridged molecules at 298 and 77 K are similar.

Pair Interaction Potentials of Colloids by Extrapolation of Confocal Microscopy Measurements of Collective Suspension Structure

A method for measuring the pair interaction potential between colloidal particles by extrapolation measurement of collective structure to infinite dilution is presented and explored using simulation and experiment. The method is particularly well suited to systems in which the colloid is fluorescent and refractive index matched with the solvent. The method involves characterizing the potential of mean force between colloidal particles in suspension by measurement of the radial distribution function using 3D direct visualization. The potentials of mean force are extrapolated to infinite dilution to yield an estimate of the pair interaction potential, U(r). We use Monte Carlo simulation to test and establish our methodology as well as to explore the effects of polydispersity on the accuracy. We use poly-12-hydroxystearic acid-stabilized poly(methyl methacrylate) particles dispersed in the solvent dioctyl phthalate to test the method and assess its accuracy for three different repulsive systems for which the range has been manipulated by addition of electrolyte.